28 citations · 154 across the 37 of their papers we have counts for
37 papers
The Calderón problem for near-Euclidean metrics
Gunther Uhlmann, Yiran Wang
In this article, we consider the anisotropic Calderón problem of determining the potential from boundary measurements of the time-independent Schrödinger equation on compact Rieman…
The partial data Calderón problem in dimension three
Gunther Uhlmann, Yiran Wang
We consider an inverse boundary value problem for the time-independent Schrödinger equation in dimension three. We prove that the local Dirichlet-to-Neumann map defined near a boun…
A clever neural network in solving inverse problems of Schrödinger equation
Yiran Wang
In this work, we solve inverse problems of nonlinear Schrödinger equations that can be formulated as a learning process of a special convolutional neural network. Instead of attemp…
Gauss Newton method for solving variational problems of PDEs with neural network discretizaitons
Wenrui Hao, Qingguo Hong, Xianlin Jin
The numerical solution of differential equations using machine learning-based approaches has gained significant popularity. Neural network-based discretization has emerged as a pow…
Inverse source problem for the Boltzmann equation in cosmology
Yiran Wang
We study the inverse problem of recovering primordial perturbations from anisotropies of Cosmic Microwave Background (CMB) using the kinetic model. Mathematically, the problem in c…
A Method for Computing Inverse Parametric PDE Problems with Random-Weight Neural Networks
Suchuan Dong, Yiran Wang
We present a method for computing the inverse parameters and the solution field to inverse parametric PDEs based on randomized neural networks. This extends the local extreme learn…
Recovery of black hole mass from a single quasinormal mode
Gunther Uhlmann, Yiran Wang
We study the determination of the mass of a de Sitter-Schwarzschild black hole from one quasinormal mode. We prove a local uniqueness result with a Hölder type stability estimate.
A conservative multiscale method for stochastic highly heterogeneous flow
Yiran Wang, Eric Chung, Shubin Fu
In this paper, we propose a local model reduction approach for subsurface flow problems in stochastic and highly heterogeneous media. To guarantee the mass conservation, we conside…
A deep learning based reduced order modeling for stochastic underground flow problems
Yiran Wang, Eric Chung, Shubin Fu
In this paper, we propose a deep learning based reduced order modeling method for stochastic underground flow problems in highly heterogeneous media. We aim to utilize supervised l…
Existence of resonances for Schrodinger operators on hyperbolic space
David Borthwick, Yiran Wang
We prove existence results and lower bounds for the resonances of Schrödinger operators associated to smooth, compactly support potentials on hyperbolic space. The results are deri…
Some integral geometry problems for wave equations
Yiran Wang
We consider the Cauchy problem and the source problem for normally hyperbolic operators on the Minkowski spacetime, and study the determination of solutions from their integrals al…
Inverse Problem of Nonlinear Schrödinger Equation as Learning of Convolutional Neural Network
Yiran Wang, Zhen Li
In this work, we use an explainable convolutional neural network (NLS-Net) to solve an inverse problem of the nonlinear Schrödinger equation, which is widely used in fiber-optic co…
A local-global generalized multiscale finite element method for highly heterogeneous stochastic groundwater flow problems
Yiran Wang, Eric Chung, Shubin Fu
In this paper, we propose a local-global multiscale method for highly heterogeneous stochastic groundwater flow problems under the framework of reduced basis method and the general…
Microlocal analysis of the light ray transform on globally hyperbolic Lorentzian manifolds
Yiran Wang
For the light ray transform on globally hyperbolic Lorentzian manifolds of dimension acting on compactly supported distributions, we show that the Schwartz kernel of t…
The anisotropic Calderón problem for high fixed frequency
Gunther Uhlmann, Yiran Wang
We consider Schrödinger operators at a fixed high frequency on simply connected compact Riemannian manifolds with non-positive sectional curvatures and smooth strictly convex bound…
Constraint energy minimization generalized multiscale finite element method in mixed formulation for parabolic equations
Yiran Wang, Eric Chung, Lina Zhao
In this paper, we develop the constraint energy minimization generalized multiscale finite element method (CEM-GMsFEM) in mixed formulation applied to parabolic equations with hete…
A comparison of mixed multiscale finite element methods for multiphase transport in highly heterogeneous media
Yiran Wang, Eric Chung, Shubin Fu
In this paper, we systemically review and compare two mixed multiscale finite element methods (MMsFEM) for multiphase transport in highly heterogeneous media. In particular, we wil…
Adaptive multiscale model reduction for nonlinear parabolic equations using GMsFEM
Yiran Wang, Eric Chung, Shubin Fu
In this paper, we propose a coupled Discrete Empirical Interpolation Method (DEIM) and Generalized Multiscale Finite element method (GMsFEM) to solve nonlinear parabolic equations…
Online conservative generalized multiscale finite element method for flow models
Yiran Wang, Eric Chung, Shubin Fu +1
In this paper, we consider an online enrichment procedure using the Generalized Multiscale Finite Element Method (GMsFEM) in the context of a two-phase flow model in heterogeneous…
Inverse Scattering for Critical Semilinear Wave Equations
Antônio Sá Barreto, Gunther Uhlmann, Yiran Wang
We show that the scattering operator for defocusing energy critical semilinear wave equations \square u+f(u)=0, with f C-infinity and f ~ u^5, in three space dimensions, determines…
Sharp resolvent estimates on non-positively curved asymptotically hyperbolic manifolds
Yiran Wang
We study the high energy estimate for the resolvent of the Laplacian on non-trapping asymptotically hyperbolic manifolds (AHM). In the literature, polynomial bound of the fo…
On the light ray transform of wave equation solutions
András Vasy, Yiran Wang
We study the light ray transform on Minkowski space-time and its small metric perturbations acting on scalar functions which are solutions to wave equations. We show that the light…
Convolutional neural networks in phase space and inverse problems
Gunther Uhlmann, Yiran Wang
We study inverse problems consisting on determining medium properties using the responses to probing waves from the machine learning point of view. Based on the understanding of pr…
Singularities generated by the triple interaction of semilinear conormal waves
Antônio Sá Barreto, Yiran Wang
We study the local propagation of conormal singularities for solutions of semilinear wave equations , where is a polynomial of degree in $…